Modular arithmetic (clock arithmetic) is a system of arithmetic of integers. The basic ingredient is the congruence relation $a \equiv b \bmod n$ which means that $n$ divides $b-a$. In modular arithmetic one can add, subtract, multiply and exponentiate but not divide in general. The Euclidean algorithm and the Chinese remainder theorem are important throughout mathematics. Modular exponentiation plays an important role in cryptography nowadays.

history | show excerpt | excerpt history